Dual parallelisms
Abstract
Assume that is a parallelism in , for a field, that admits a collineation group that fixes one spread and acts transitively on the remaining spreads of . If contains suitable central collineations of then it is shown that the dual parallelism is a parallelism that can never be isomorphic to the original. The results show that the Johnson parallelisms of Hall or Knuth type, the Johnson-Pomareda parallelisms of type and all of the "derived" parallelisms produce dual parallelisms which are parallelisms but are nonisomorphic to the original parallelism.
DOI Code:
10.1285/i15900932v21n1p137
Keywords:
Parallelisms; Dual parallelisms
Classification:
51E23; 51A40
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